# Chapter 1. Figure It Out 8.2

## 1.1Screen 1 of 3

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Cardboard boxes are produced in a perfectly competitive market. Each identical firm has a short-run total cost curve of TC = 3Q3 – 18Q2 + 30Q + 50, where Q is measured in thousands of boxes per week. The firm’s associated marginal cost curve is MC = 9Q2 – 36Q + 30.

## 1.2Screen 2 of 3

What level of output would a firm in the cardboard box industry choose if it wanted to minimize its average variable cost of production?

### Question

To minimize average variable cost, the firm should produce 607M7xmPORU= units of output.

When AVC is at its minimum, MC = AVC. Substitute the expressions for MC and AVC to find that 9Q2 – 36Q + 30 = 3Q2 – 18Q + 30. Solve for Q to find that, when MC and AVC are equal (and AVC is it its minimum), Q = 3. For further review, see section “Average and Marginal Costs”.

## 1.3Screen 3 of 3

Calculate the price below which a firm in the market will not produce any output in the short run (the shut-down price).

### Question

The shut-down price is \$ Q1FdPC+1WRw=

The firm should stop production if the price it receives for its cardboard boxes is insufficient to cover its average variable costs. The firm’s average variable costs are AVC = 3Q2 – 18Q + 30; they are minimized at output level Q = 3. Substitute 3 for Q in the formula for average variable cost to find the lowest possible AVC which is \$3. So, if the price is below \$3, the firm will not, at any output level, be able to cover its variable costs and it should shut down. For further review, see section “Profit Maximization in a Perfectly Competitive Market.”